Question

Suppose we have the following:

S&P 500 index value = 3,104.75

Strike price: 3,000

Time until expiration: 120 days

Risk free rate = 2%

Volatility = .10

What is the delta of a PUT option given these characteristics?

	A.	.2468
	B.	-.2468
	C.	.2290
	D.	-.2290

Answer 1

Delta of a put option = N(d1) - 1

where :

d1 = (ln(S0 / K) + (r + σ2/2)*T) / σ√T

S0 = current spot price

K = strike price

r = risk-free interest rate

T is the time to expiry in years

σ = standard deviation of underlying asset returns

N(x) is the cumulative normal distribution function

First, we calculate d1 as below :

· ln(S0 / K) = ln(3104.75 / 3000). We input the same formula into Excel, i.e. =LN(3104.75 / 3000)

· (r + σ2/2)*T = (0.02 + (0.102/2)*(120/365)

· σ√T = 0.10 * √(120/365)

d1 = 0.7419

N(d1), is calculated in Excel using the NORMSDIST function and inputting the value of d1 into the function.

N(d1) = 0.7710

Delta of a put option = N(d1) - 1

Delta of a put option = 0.7710 - 1

Delta of a put option = -0.2290

The answer is D